Bulletin of the
Korean Mathematical Society BKMS

In this paper, we prove that there is no branch point in the Lorentz space $(M,d)$ which is the limit space of a sequence $\{(M_\alpha,d_\alpha)\}$ of compact globally hyperbolic interpolating spacetimes with $C^{\pm}_\alpha$-properties and curvature bounded below. Using this, we also obtain that every maximal timelike geodesic in the limit space $(M,d)$ can be expressed as the limit curve of a sequence of maximal timelike geodesics in $\{(M_\alpha,d_\alpha)\}$. Finally, we show that the limit space $(M,d)$ satisfies a timelike triangle comparison property which is analogous to the case of Alexandrov curvature bounds in length spaces.

Keywords: Lorentzian Gromov-Hausdorff theory, timelike triangle compari\-son

MSC numbers: Primary 53C20; Secondary 57S20